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Question

Two spherical conductors A1 and A2 of radii r1 and r2(r2>r1) are placed concentrically in air. A1 is given a charge +Q while A2 is earthed. Then the equivalent capacitance of the system is:

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A
4πϵ0r1r2r2r1
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B
4πϵ0(r1+r2)
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C
4πϵ0r2
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D
4πϵ0r1
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Solution

The correct option is A 4πϵ0r1r2r2r1
By Gauss's law the electric field at a distance r in between the shells is
E.4πr2=Qϵ0E=Q4πϵ0r2
The potential difference between shells is V0dV=r1r2Edr
or V=Q4πϵ0r1r2drr2=Q4πϵ0(1r11r2)
or V=Q4πϵ0.r2r1r1r2
Capacitance, C=QV=4πϵ0r1r2r2r1

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